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# Bruhat Order on the Involutions of Classical Weyl Groups

@inproceedings{IncittiBruhatOO, title={Bruhat Order on the Involutions of Classical Weyl Groups}, author={Federico Incitti} }

It is known that a Coxeter group W , partially ordered by the Bruhat order, is a graded poset, with rank function given by the length, and that it is EL-shellable, hence CohenMacaulay, and Eulerian. In this work we consider the subposet of W induced by the set of involutions of W , denoted by Invol(W ). Our main result is that, if W is a classical Weyl group, then the poset Invol(W ) is graded, with rank function given by the average between the length and the absolute length, and that it is EL… CONTINUE READING